Spectral gap in the group of affine transformations over prime fields

Abstract

We study random walks on the semi-direct product of F_p^d and SL_d(F_p). We estimate the spectral gap in terms of the spectral gap of the projection to the linear part SL_d(F_p). This problem is motivated by an analogue in the isometry group of Euclidean space, which have application to smoothness of self-similar measures.

25 pages, final version, results are unchanged, modified the argument relating L^2 and L^4 estimates using the Riesz-Thorin theorem, rest of the arguments are unchanged

References in corpus (2)

• Growth in finite simple groups of Lie type of bounded rank
• Random walks in the group of Euclidean isometries and self-similar measures

Cited by in corpus (3)

• Random walks in the group of Euclidean isometries and self-similar measures
• Affine random walks on the torus
• Towards super-approximation in positive characteristic